 |
| Eolian's low aspect ratio propeller |
I've been thinking about propellers lately. A lot.
No, I can't explain that. Perhaps it is a residue of our recent election. Or something.
Nevertheless...
Now, I am not a trained Naval Architect. But still, I have thoughts which seem coherent (to me at least, but then the judge may be biased), some brought on by casual observation of a rooster tail following a heavy cruiser. Even riding on a ferry you can see evidence of a jet of water that eventually surfaces astern.
To me, the whole idea of thinking of a propeller as a water screw is, well, screwed.
Imagine that the that theoretical speed of a boat which would be determined only by the pitch of the prop and its RPM is called St. In the common parlance, "slippage" - that condition when the boat is moving at less than St, is considered to be an inefficiency.
But imagine that a boat is moving thru the water at exactly St... there is zero "slippage" - the prop is a perfect screw. But then the only force on the prop is drag, as it completes its revolutions thru the water. So how then is any force created* to move the boat forward?
How about this instead: Newton's Third Law: For every action there is an equal and opposite reaction. Imagine now that the prop's mission in life is to throw as much water astern as it can... in a sense the boat becomes a rocket, propelled by the water being thrown away aft. This theory would have as a consequence that "slippage" is required for propulsion. If the boat reaches St, from the boat's perspective NO water is being thrown aft... NO propulsion. This also says that a boat will never reach St, because the closer it gets, the less propulsive force is available - a hydraulic version of Zeno's Paradox.
Given a fixed amount of horsepower applied to the shaft, the product of the amount of water discharged and its speed are fixed. If you want more water discharged, then for a fixed amount of horsepower input, the discharge speed of the water must be decreased. And vice versa. So, if you want a high speed discharge jet (high St), you must compromise with less water in the jet. Therefore, assuming the same Chevy V8 engine, installed in a high-speed racing hydrofoil, you'll need a comparatively small diameter prop with a HUGE pitch. With that same engine in a tug, a large, slow-turning prop will give you humongous thrust, but with the compromise of a low top speed. Variable pitch props do not solve the problem because they only allow their pitch to be changed, not their diameter.
What do you need for your boat? I bet that you want the most speed you can get. So: the highest pitch prop that still provides sufficient thrust to get you somewhere near St for that pitch. Still a guessing game, tho empirical formulae do exist.
*I said that at St there would be no thrust. That is not (at least theoretically) true. Since the beginning of flight, aircraft propeller blades have had an airfoil cross section. That is, they are really rotating wings, not only generating thrust by virtue of their pitch, but also using the pressure differential the airfoil creates between the front of the prop blades and the rear: lift. An aircraft propeller, even operating at (or above!) St still delivers thrust because of this. It strikes me that there is a lot of room for hydrodynamic improvement in water propellers, specifically in improving their lift/drag ratios. Aircraft wings and propellers (and sailboat keels!) long ago gave up the low aspect ratio shape that today's boat propellers still retain. Continuing with that thought, boat propellers, it would seem to me, would be well served if they moved toward narrow high aspect ratio blades with a cross sectional shape derived from hydrofoils. Another trade-off: enough "meat" will need to be retained in those thin blades to handle the thrust forces...
Posts
9 comments:
You need to play you guitar more, Bob. Your left brain is taking over.
Although I know all of the standard aerodynamic theory (chemical engineer--we do a lot with flow), have a similar viewpoint on sails, also based on conservation of momentum:
Air approaches the boat. The sails turn the air. The more air we can turn, and the better the reaction force is aligned with the forward direction, the better we go. Perhaps it helps to envision the mythical bucket whirled around your head. It doesn't describe head sail interactions and flow separation so well, but I think it is a better way of getting your arms around a spinnaker sometimes.
An over simplification, to be certain, but while sailing I don't need to be doing higher math. Simple visualizations work better. Turn air, go forward.
I enjoyed reading your post, but I did have a few thoughts. You mention that a variable pitch prop wont make a difference because the diameter doesn't change, however to continue you comparisons. Aircraft do have a variable pitch prop called a CS Prop or constant speed prop, where the pilot can tune the prop to the conditions of the aircraft and atmosphere. Given there are obvious differences between hydrodynamics and aerodynamics one does wonder if the base principles can be the same as in both cases the prop is cutting trough mass (air or water) to provide thrust. I also wonder how the dynamics come into play with dual counter rotating props, especially when applied the idea of variable pitch.
Thanks for posting, it was an entertaining break from work today. :)
Hi Ted - thanks for your kind words!
All of my musings were with the assumption that the engine was fully loaded, I guess I should have mentioned that somewhere. My bad. But now having said that, if a prop is taking full engine output at minimum pitch, increasing the pitch will drag the engine down lower in the power band, decreasing the available horsepower.
If the engine is operating at max power at full pitch, decreasing the pitch will cause an overspeed, or with a governed engine a decrease in horsepower because the throttle will partly close - this is the situation on airplanes with constant speed props.
For optimum behavior, an imaginary prop would increase blade length while pitch was decreased such that full engine horsepower was absorbed at all times, allowing thrust vs speed tradeoffs while keeping full engine output. Now that I think about that, a CVT automatic transmission would probably also be needed to get the most out of the prop/engine combination.
I, also not a Naval Architect, think you're missing one aspect of the St vs boat speed comparison. You say that when St is reached there would be no thrust generated. With a screw analogy that is true, but the only way to do that would be to have zero drag on the boat and prop. And in this ideal frictionless/dragless world, once the boat achieved that speed you would not need any thrust, as the system would be in equilibrium and the boat would continue on until another force acted on it.
In this dragless world, you could shut your engine down as soon as you were going as fast as you wanted. Obviously, we don't live in a drag free world, so our inefficiency or slippage is really just a measure of how responsive a prop is to a reduction in boat speed caused by drag.
I do think the rocket thrust analogy is a good one, and you are more than correct in saying a pitch and diameter change is necessary to utilize full HP at varying speeds.
You're also right on about the inefficiencies of boat props. High aspect ratio blades would be much more efficient, but the stresses applied by the water and the need for a smaller size because of draft restrictions limit the efficacy of this idea. However, if you crack open a jet-drive you will find exactly these things, ie. high aspect ratio blades, short enough that they can withstand the stress. They make up for their lack of total length by having many more blades, and the housing eliminates the dreaded tip-vortexes that kill the effective area of any high aspect ratio airfoil.
Perhaps a more efficient prop could be made with, say, 12 high aspect blades with a containing ring attached to the outer tips to help efficiency. This would have the added benefit of never being able to snag a crab pot.
Absolutely Capt. Straw! I've long wondered why props don't come with a cast-in-place tip ring - it's the ultimate answer to tip vortices!
Bob,
I've been following your blog for some time and I think you're right on the money re the prop as a pump not a screw, I've discussed this very thing on my blog (yet in it's infancy)see here http://kmnsmallboatdesigns.blogspot.ca/2016/10/wheel-of-deal.html. I don't know that more blades and a confining ring would be good for a sail boat, more drag when sailing. A power boat is another matter altogether.
Kevin McNeill
Hi Kevin!
Enjoyed your blog (I'm following now)!
Adding blades has always seemed like a crapshoot... at some point you have so many blades that each is operating in the slipstream from the previous one. In wind turbine design anyway, the most efficient design (whatever that means...) is for a single blade (balanced by a counterweight, of course), but you never see one of those...
As for the tip fence, I do believe that all props should have them. They need not be heavy - sheet metal thick enough to stand up to the intended abuse would be enough. And with the fence, the elliptical design of the propeller blades, developed as a means of decreasing the inevitable tip vortex generation, would not be required, and probably not optimal to boot.
As far as drag is concerned, I think that the added wetted surface drag from the tip fence ring itself would be negligible compared to that from the blades. But wait... Hmmm... by making the blades more efficient when they are powered, that might make them have higher drag when they are not... Experimentation is called for. And I do think that an integral ring would be an improvement over a stationary shroud because the inevitably required clearance between the blade tips and the shroud would be turbulence zone, sucking engine power just to stir water.
bob
s/v Eolian
Anacortes
Post a Comment